Heat oil in heavy pot. Add carrot, celery and onion; sauté until vegetables are softened, 4 to 5 minutes. Add garlic; sauté 1 minute longer.
Add tomatoes, beef broth, sugar, salt and pepper. Bring to boiling over medium heat. Reduce heat; simmer, uncovered, 45 to 60 minutes or until mixture thickens slightly. Use for Swiss steak or short ribs, or cool to room temperature, then refrigerate, covered, for later use.
Combine flour, salt and pepper in small bowl. Coat steak on both sides with flour mixture. Pound both sides with meat mallet. Coat large heavy skillet with nonstick cooking spray. Heat oil in skillet. Add steak; brown on both sides. Pour in Jardiniere Sauce. Cover and simmer for 1-1/2 hours or until steak is tender. Uncover; simmer for 30 minutes or until sauce has thickened slightly.
Brown short ribs, working in batches if necessary, in Dutch oven or other large flameproof, ovenproof casserole, over medium heat. Add Jardinière Sauce. Bring to simmering. Cover; bake in 375°F oven 2 hours or until meat is tender. Skim fat from top. Check liquid after 1 hour; add a little water if mixture looks too dry.